46. If (x – 2) (x – p) = x² – ax + 6, then the value of (a – p) is

1. 1. 0

   
   
   

   2. 1

   
   
   

   3. 2

   
   
   

   4. 3

   
   
   

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1. View Hint View Answer Discuss in Forum

   (x – 2) (x – p) = x² – ax + 6
   ⇒  x (x – p) –2 (x – p)
   = x² – ax + 6
   ⇒  x² – px – 2x + 2p = x² – ax + 6
   ⇒  x² – x (p + 2) + 2p
   = x² – ax + 6
   ∴  p + 2 = a
   (comparing respective co-efficients)
   ⇒  a – p = 2

   Correct Option: C

   (x – 2) (x – p) = x² – ax + 6
   ⇒  x (x – p) –2 (x – p)
   = x² – ax + 6
   ⇒  x² – px – 2x + 2p = x² – ax + 6
   ⇒  x² – x (p + 2) + 2p
   = x² – ax + 6
   ∴  p + 2 = a
   (comparing respective co-efficients)
   ⇒  a – p = 2

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47. If	1	+ x2 represents the redius of circle P and	1	+ x = 17,
    	x2		x

    which of the following best approximates the circumference of circle P ?

1. 1. 287 π

   
   
   

   2. 547 π

   
   
   

   3. 574 π

   
   
   

   4. 278 π

   
   
   

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1. View Hint View Answer Discuss in Forum

   1	+ x = 17
   x

   
   On squaring both sides,
   

   	x +	1		2	= 172
   		x

   
   

   ⇒	1	+ x2 + 2 = 289
   	x2

   
   

   ⇒	1	+ x2 = 289 − 2 = 287
   	x2

   
   = radius of the circle
   ∴  Circumferece of circle = 2πr
   = 2 × 287 × π
   = 574π units

   Correct Option: C

   1	+ x = 17
   x

   
   On squaring both sides,
   

   	x +	1		2	= 172
   		x

   
   

   ⇒	1	+ x2 + 2 = 289
   	x2

   
   

   ⇒	1	+ x2 = 289 − 2 = 287
   	x2

   
   = radius of the circle
   ∴  Circumferece of circle = 2πr
   = 2 × 287 × π
   = 574π units

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48. If	a	=	1	, find the value of the expression	(2a − 5b)
    	b		2		(5a + 3b)

1. 1. –32

   
   
   

   2. 11

   
   
   

   3. −8

      11

   
   
   

   4. 17

   
   
   

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1. View Hint View Answer Discuss in Forum

   a	=	1
   b		2

   
   
   

   =	2 ×	1	− 5
   		2
   	5 ×	1	+ 3
   		2

   
   

   =	1 − 5						=	− 4 × 2
   	5	+ 3						5 + 6
   	2

   
   

   −8

   11

   Correct Option: C

   a	=	1
   b		2

   
   
   

   =	2 ×	1	− 5
   		2
   	5 ×	1	+ 3
   		2

   
   

   =	1 − 5						=	− 4 × 2
   	5	+ 3						5 + 6
   	2

   
   

   −8

   11

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49. If   a +	1	= 1 and b +	1	= 1 then c +	1	is equal to :
    	b		c		a

1. 1. 1

   
   
   

   2. 0

   
   
   

   3. –1

   
   
   

   4. 2

   
   
   

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1. View Hint View Answer Discuss in Forum

   a +	1	= 1
   	b

   
   

   ⇒  a = 1 –	1	=	b − 1
   	b		b

   
   

   ∴	1	=	b
   	a		b − 1

   
   

   Again, b +	1	= 1
   	c

   
   

   ⇒	1	= 1 – b
   	c

   
   

   ⇒  c =	1
   	1 – b

   
   

   ∴  c +	1	=	1	+	b
   	a		1 – b		b − 1

   
   

   =	1	−	b	=	1 – b	= 1
   	1 – b		1 – b		1 – b

   Correct Option: A

   a +	1	= 1
   	b

   
   

   ⇒  a = 1 –	1	=	b − 1
   	b		b

   
   

   ∴	1	=	b
   	a		b − 1

   
   

   Again, b +	1	= 1
   	c

   
   

   ⇒	1	= 1 – b
   	c

   
   

   ⇒  c =	1
   	1 – b

   
   

   ∴  c +	1	=	1	+	b
   	a		1 – b		b − 1

   
   

   =	1	−	b	=	1 – b	= 1
   	1 – b		1 – b		1 – b

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50. The value of	a	+	b	is
    	a − b		b − a

1. 1. (a + b)

      (a − b)

   
   
   

   2. –1

   
   
   

   3. 2ab

   
   
   

   4. 1

   
   
   

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1. View Hint View Answer Discuss in Forum

   Expression =	a	+	b
   	a − b		b − a

   
   

   =	a	−	b
   	a − b		a − b

   
   

   =	a − b	= 1
   	a − b

   Correct Option: D

   Expression =	a	+	b
   	a − b		b − a

   
   

   =	a	−	b
   	a − b		a − b

   
   

   =	a − b	= 1
   	a − b

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